The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100. . What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

b. What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

c. What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

d. Which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to have at least a .95 probability that the sample mean is within $16 of the population mean?